1 / 49

9.5 = Variation Functions

9.5 = Variation Functions. Direct Variation. Direct Variation – y varies directly as x. Direct Variation – y varies directly as x y = k x. Direct Variation – y varies directly as x y = k x * Note: k = constant of variation (a #).

Download Presentation

9.5 = Variation Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 9.5 = Variation Functions

  2. Direct Variation

  3. Direct Variation – y varies directly as x

  4. Direct Variation – y varies directly as x y = kx

  5. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #)

  6. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation

  7. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x

  8. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x

  9. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation

  10. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z

  11. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z y = kxz

  12. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.

  13. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

  14. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

  15. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 a

  16. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse a

  17. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a

  18. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x

  19. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x

  20. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct

  21. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5

  22. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh

  23. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint

  24. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint , k = ½

  25. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

  26. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

  27. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

  28. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

  29. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15)

  30. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k

  31. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18= k 15

  32. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18= k 15 6= k 5

  33. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx2) y = kx 18 = k(15) 18 = 15k 18= k 15 6= k 5

  34. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k 15 6= k 5

  35. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k 15 6= k 5

  36. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k 5

  37. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k y = 120 5 5

  38. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k y = 120 5 5 y = 24

  39. Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  40. 1) y = kxz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  41. 1) y = kxz -90 = -6(15)k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  42. 1) y = kxz -90 = -6(15)k -90 = -90k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  43. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  44. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  45. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  46. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  47. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21

  48. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k

  49. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k 2) y = k x 21 = -168 x x = -8

More Related